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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 443982o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443982.o4 | 443982o1 | \([1, 0, 1, 3343, 45620]\) | \(4657463/3696\) | \(-3280213604976\) | \([2]\) | \(967680\) | \(1.0895\) | \(\Gamma_0(N)\)-optimal* |
443982.o3 | 443982o2 | \([1, 0, 1, -15877, 391580]\) | \(498677257/213444\) | \(189432335687364\) | \([2, 2]\) | \(1935360\) | \(1.4361\) | \(\Gamma_0(N)\)-optimal* |
443982.o1 | 443982o3 | \([1, 0, 1, -217687, 39058376]\) | \(1285429208617/614922\) | \(545745538527882\) | \([2]\) | \(3870720\) | \(1.7827\) | \(\Gamma_0(N)\)-optimal* |
443982.o2 | 443982o4 | \([1, 0, 1, -121587, -16056896]\) | \(223980311017/4278582\) | \(3797257274460342\) | \([2]\) | \(3870720\) | \(1.7827\) |
Rank
sage: E.rank()
The elliptic curves in class 443982o have rank \(0\).
Complex multiplication
The elliptic curves in class 443982o do not have complex multiplication.Modular form 443982.2.a.o
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.